Thermomechanical Damage
From Microstructure to FE-Analysis
In the last years the increasing demands on engine efficiency and specific power have resulted
in progressively higher loadings on internal components of combustion engines. Especially
downsizing in gasoline and diesel engines has made thermomechanical lifetime a critical design
issue. Therefore the durability assessment of such components is increasingly in demand,
trig-gered by both reliability and economic requirements. The methodology developed at BMW
power train for the fatigue assessment is with particular emphasis on the thermo-mechanical
fatigue (TMF) aspect.
caused by cyclic temperature variations coming from the hot/cold cycles induced by the start-stop operation and the tran-sient load variation during engine opera-tion. The calculation of the cyclic tem-perature field is a complex task involving the use of computational fluid dynamic (CFD), conjugate heat transfer (CHT) and non-linear finite element (FE) analysis tools for the different components under consideration.
After a brief description of both the material and the CAE TMF process atten-tion is given to the local damage evolu-tion in aluminium silicon cylinder head alloys under thermo mechanical load-ing. Microstructural investigations in specimens as well as cylinder heads un-der engine loading are shown. Strain controlled TMF tests were carried out varying mechanical strain amplitudes and maximum temperature independ-ently to identify the controlling mecha-nism for the damage evolution. The dam-age evolution is finally modelled with a Dowling type parameter based on the growth of micro-cracks.
produced in different casting technolo-gies, using aluminium-silicon-copper (Al-Si-Cu) and aluminium-silicon-magnesi-um alloys (Al-Si-Mg). Besides their good castability they stand out for favourable thermo physical attributes and static properties like tensile strength and duc-tility, which can be influenced by a heat treatment in a large range. The dendrite structure constitutes of the primary alu-minium matrix and the alualu-minium-sili- aluminium-sili-con eutectic with different intermetal-lics, like Al2Cu and AlMnFeSi phases,
Figure 1. Aluminium-silicon alloys are pri-marily precipitation hardened. The me-chanical properties and the fracture be-haviour are directly connected to the microstructure. Coarse intermetallics and the eutectic silicon, as well as the po-rosity determine the fatigue and fracture behaviour [1].
3 TMF CAE Process
The analysis of TMF life of cylinder heads is a complex task, considering the
differ-Figure 1: Microstructure of a secondary Aluminium-Silicon-Copper alloy
Dipl.-Ing. Sebastian Thalmair works for CAE crank drive and cylinder head gasoline engines at BMW Group in Munich (Germany).
Dr. Andreas Fischers-worring-Bunk is Head of CAE crank drive and cylinder head gasoline engines at BMW Group in Munich (Germany). Dr. Franz-Josef Klinkenberg is Head of Metallurgy in the light-metal foundry at BMW Group in Munich (Germany). Dr. Karl-Heinz Lang is Head of fatigue de-partment Institut für Werkstoffkunde I Uni-versität Karlsruhe (tH) (Germany).
ent steps involved in the calculation pro-cedure. The thermo-mechanical fatigue problem originates from the cyclic
ther-mal load. This load is calculated employ-ing a software tool for the analysis of the gas exchange process, a tool for the
three-dimensional simulation of combustion to get local heat transfer information, a tool for the CFD analysis of the water jacket and conjugated heat transfer anal-ysis for the temperature field prediction in the fluid flow and structure. A non-linear FE code is used for the structural finite element analysis. The structural FE analysis includes the identification and application of the thermo-mechanical loading. As the calculated lifetime is very sensitive on the thermal load, the ther-mal model therefore is the key factor.
Aluminium shows the effect of age-ing as well as viscous effects at the rele-vant operating temperatures. Depending on the alloy and heat treatment, differ-ent complexities of the constitutive model can be required. Alternative com-binations of constitutive model and age-ing model are used, rangage-ing from elas-tic-plastic models with a nonlinear kin-ematic hardening to simple elasto-visco-plastic ones [2, 3, 4]. The change in yield strength by ageing may affect the non-linear compliance redistribution in the component and therefore the resulting mechanical strain amplitude in critical areas.
For the cylinder head life assessment a damage parameter derived form the cyclic J-integral for the growth of micro-cracks is used. Initially Heitmann [5] de-fined this parameter for the use with steels. This parameter is composed of a plastic and an elastic part and was adapt-ed for the use with aluminium-silicon alloys [2].
4 Experimental Details
TMF-tests were performed in an electro-mechanical testing machine. To reach the required cooling and heating rate of 10 K/s, a 5 kW inductive heater and forced air cooling was used. The strain was measured with a capacitive exten-someter. The force was determined with a 100 kN load cell and the temperature was measured with a Ni-CrNi ribbon-type thermocouple. At the beginning of each test, the thermal strain εth of the speci-men as a function of temperature was determined by reference temperature cy-cles at zero force. Afterwards, the ma-chine was switched to strain control and the total strain εt was controlled in such
Figure 2: TMF crack initiation in an Aluminium Silicon alloy [6]
Figure 3: TMF crack path following brittle eutectic phases
a way that the total mechanical strain εtme is phase shifted by 180° against the thermal strain, according to the relation-ship εt = εt,me + εth. A set of TMF-tests on an Al-Si-Cu alloy was performed to
deter-mine the influence of the total mechani-cal strain amplitude and the maximum temperature (Tmax) of the TMF-cycles on the lifetime-behaviour, while all other test parameters remain constant. These
ing with εt,me = 0 at Tmin = 50 °C. The me-chanical strain amplitude was varryied up to εa,tme = 0,5 % independently of tem-perature.
5 Damage Evolution in
Aluminium-silicon Alloys
In recent years the microstructural dam-age evolution in Aluminium-Silicon al-loys was investigated in a series of re-search programs at the University of Karlsruhe [7, 8, 9]. Under TMF conditions distinct plastic deformation, caused by the TMF-load, results in crack initiation due to a separation of silicon particles from the aluminium matrix early com-pared to the macroscopic observed life-time, Figure 2. The separation is a result of the significant unequal thermal ex-pansion coefficient of aluminium and silicon, which leads to stressing of the interface with each thermal cycle and therefore to a separation during thermal loading. The following crack-propagation mainly occurs along brittle phases in the eutectic structure, Figure 3.
Figure 4 shows the microstructural damage evolution in a cylinder head. The cylinder head was run in a thermal shock engine test and showed signs of plastic deformation in the intervalve re-gion, but no macroscopic crack initia-tion. Detailed metallographic investiga-tions revealed initiated cracks on the microscopic scale even well below the surface. The observed crack initiation sites and propagation schemes are com-parable to the observed damage in the TMF experiments.
6 Description of Damage
The results of the different TMF-test pa-rameters on the observed fatigue life are given in Figure 5. Diagrams for mechani-cal and plastic strain amplitude, Smith-Watson Topper and Ostergren parame-ters versus the number of cycles to fail-ure are shown. The rise of Tmax from 200 °C to 250 °C leads to an increase in lifetime for all strain amplitudes. There-fore a description of lifetime just by use
Figure 4: TMF crack initiation in a cylinder head
Figure 5: Mechanical and plastic strain amplitudes, Smith-Watson Topper and Ostergren parameters versus the number of cycles to failure for TMF experiments varying temperature and mechanical strain independently
of the mechanical and plastic strain am-plitude is not possible. Due to the poor correlation the use of the Ostergren pa-rameter in the form of
POST = σMAX εa,pl Eq. (1) as an approximation for the dissipated energy allows no description of lifetime, as can be seen in Figure 5. The Smith-Watson-Topper parameter shows the best correlation with lifetime. This indicates a strong dependency of damage evolu-tion in aluminium-silicon alloys on the macroscopic maximum induced stresses, viz. strain energy density. The parameter of Smith-Watson-Topper is used in the following form:
PSWT = σMAX εa,me Eq. (2) In these relations εa,me, εa,pl and σMAX are the mechanical, plastic strain ampli-tudes and the maximum stress of the cy-cle respectively.
Based on this observation the depend-ency of fatigue life was modelled by adapting a energy parameter for the cyclic J integral like proposed by Dowling in [10].
ΔJ = fl We + Wp Eq. (3)
The elastic energy was calculated as
We = σ
2 max
____ 2E Eq. (4)
In [11] the dissipated energy per cycle is proposed to describe the lifetime behav-iour, it is calculated in our case as
Wp =
∫
σ ∙ & dt Eq. (5) where We and Wp are the elastic and plastic energy, E the Young’s modulus and f1 a material constant. The parame-ter allows describing the lifetime depend-ency of the TMF experiments, as well as the lifetime of isothermal Low cycle fa-tigue experiments at room temperature,Figure 6. This indicates that the combina-tion of dissipated plastic energy and in-duced stress is responsible for both life-time dependencies. The complex interac-tion of ageing, temperature, crack initia-tion and crack growth will require ques-tioning the applicability of the deforma-tion and damage model in each case for aluminium-silicon alloys.
7 Conclusion
The observed micro crack initiation in cylinder heads is of the same type as the observed damage in the TMF specimens. The study of the effect of maximum tem-perature and mechanical strain ampli-tude showed the strain energy density and the maximum induced stresses as the controlling factors on TMF fatigue life in the investigated Al-Si-Cu alloy. The resulting damage modelling confirms
the already applied cyclic J-integral dam-age concept. Applied in engine projects the adapted energetic Heitmann param-eter showed a good quality of its predic-tive capabilities.
References
[1] thalmair, S.; Fischersworring-Bunk, A.; Klinken-berg, F-J.; lang, K.-H.; löhe, D.: Materialprüfung, 49, 2007, 113-117
[2] thalmair, S. Fischersworring-Bunk, A. thiele, J. Ehart, R. Guillou, M.: SAE World Congress 2006, Detroit, USA, April 3-6, 2006-01-0541, 2006 [3] thalmair, S.; Fischersworring-Bunk, A.; lang, K.;
löhe, D.: proc. Intl. Fatigue Conf. 2006, Atlanta, USA, 14-19 May, 2006
[4] Ehart, R.; nefischer, p.; Riedler, M.: Betriebsfestig-keit in der virtuellen produktentwicklung, Steyr, oct. 11.-12., 33. tagung DvM-Arbeitskreis Be-triebsfestigkeit, 2006
[5] Heitmann, H.H.; vehoff, H.; neumann, p.: 6th Int. Conf. on Fracture, 1984
[6] luft, J.; Beck, t.; löhe, D.: 11th Int. Conf. on Frac-ture, turin, Italy, March 20-25, 2005
[7] Flaig, B.: Isothermes und thermisch-mechanisches Ermüdungsverhalten von GK-AlSi10Mg wa, GK-Al-Si12CuMgni und GK-AlSi6Cu4, phD thesis, Univer-sität Karlsruhe (tH), 1995
[8] luft, J.; Beck, t.: Weiterentwicklung des Al-leich-tbaus für motorische Hochleistungskomponenten mit Hilfe einer neuen tMF/HCF Methode, BMBF verbundprojekt 03n3095, Universität Karlsruhe (tH), 2005
[9] Henne, I.: Schädigungsverhalten von Aluminium-gusslegierungen bei tMF und tMF/HCF-Beans-pruchung, phD thesis, Universität Karlsruhe (tH), 2006
[10] Dowling, n.E.: Journal of Materials, 7, 1972, 71-87 [11] Charkaluk, E.; Bignonnet, A.M.; Constantinescu, A.;
Dang van, K.: Fatigue Fract. Engng. Mater. Struct., 25, 1199-1206
Figure 6: TMF and LCF tests
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